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1
Bring the water or light broth to a rolling boil in a wide, heavy pot. Season with salt. Add the bitter greens and cook for 5 minutes. They are ready when the stems yield without resistance when pressed against the side of the pot and the liquid has taken on a faint green, bitter aroma.
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2
Add half the olive oil to the pot. Drop in the broken bread pieces in a single layer. Do not stir. Allow the bread to absorb the liquid for 1–2 minutes, then apply gentle pressure with the back of a spoon to break the pieces into soft, irregular masses. This is where the dish lives or dies: too much agitation at this stage produces a uniform porridge; the correct texture retains soft but distinct pockets of bread among the greens.
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3
Continue cooking over moderate heat, pressing gently once or twice more, until the bread has dissolved sufficiently to thicken the liquid to a loose, spoonable consistency. The surface should move slowly when the pot is tilted — neither a broth nor a stiff paste.
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4
Ladle into deep bowls. Pour the remaining olive oil — at least 3–4 tablespoons in total across four bowls — directly over each portion at the table. The oil should pool visibly on the surface. Serve immediately.